Works fine in IE, closes immediately after opening in Firefox:

 

$("#dialog-test").dialog({
      autoOpen: false,
      title: 'User Information',
      buttons: {
          'Accept': function() {
              document.getElementById("userName").value = document.getElementById("email").value;
              document.getElementById("userPw").value = document.getElementById("password").value;
              document.getElementById("userSecret").value = document.getElementById("secret").value;
               $(this).dialog('close');
           },
          Cancel: function() {
                 $(this).dialog('close');
          }

 }});
 
$('#opener')
        .click(function() {
          $('#dialog-test').dialog('open');

});

</script>
<div id="dialog-test">

      <form>
             <div>
                    <label >Email: </label>
                    <input type="text" name="email" id="email" value="" class="text ui-widget-content ui-corner-all" /><br /><br />
                    <label >Password: </label>
                    <input type="password" name="password" id="password" value="" class="text ui-widget-content ui-corner-all" /><br /><br />
                    <label >Favorite Color: </label>
                    <input type="text" name="secret" id="secret" class="text ui-widget-content ui-corner-all" /><br /><br />
             </div>
       </form>
</div>

...

<button id="opener">Open the dialog</button>